cp's OEIS Frontend

A134602 Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).

%I A134602 #18 Apr 08 2025 23:29:38
%S A134602 378,455,527,918,1265,1615,2047,2145,2175,2345,2665,3713,3835,4207,
%T A134602 4305,4633,5000,5117,5382,6061,6678,6887,6965,7055,7267,7327,7497,
%U A134602 7685,7791,8470,8785,8918,9641,10205,10545,10647,11137,11543,11713,13482,14079
%N A134602 Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
%C A134602 Numbers included in A134600, but not in A134601. a(1)=378 is the minimal number with this property.
%C A134602 Also numbers included in A134603, but not in A134604.
%H A134602 Hieronymus Fischer, <a href="/A134602/b134602.txt">Table of n, a(n) for n = 1..10000</a>
%e A134602 a(2)=455, since 455=5*7*13 and sqrt((5^2+7^2+13^2)/3)=sqrt(81)=9.
%t A134602 f[{a_,b_}]:=Table[a,b];Select[Range[2,14079],!PrimeQ[#]&&!PrimeQ[ RootMeanSquare[f/@FactorInteger[#]//Flatten] ]&&IntegerQ[ RootMeanSquare[f/@FactorInteger[#]//Flatten] ]&] (* _James C. McMahon_, Apr 08 2025 *)
%Y A134602 Cf. A001597, A025475, A134333, A134344, A134376.
%Y A134602 Cf. A134600, A134604, A134608, A134611, A134617, A134619, A134621.
%K A134602 nonn
%O A134602 1,1
%A A134602 _Hieronymus Fischer_, Nov 11 2007
%E A134602 Definition clarified by _Hieronymus Fischer_, Apr 20 2013, Jun 01 2013